Related Experiment Video
Updated: Aug 7, 2025

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators
Published on: August 15, 2014
Complex dynamics and Bogdanov-Takens bifurcations in a retarded van der Pol-Duffing oscillator with positional
Mohammad Sajid1, Sahabuddin Sarwardi2, Ahmed S Almohaimeed3
1Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia.
Abstract:
In this article, we will investigate a retarded van der Pol-Duffing oscillator with multiple delays. At first, we will find conditions for which Bogdanov-Takens (B-T) bifurcation occurs around the trivial equilibrium of the proposed system. The center manifold theory has been used to extract second order normal form of the B-T bifurcation. After that, we derived third order normal form. We also provide a few bifurcation diagrams, including those for the Hopf, double limit cycle, homoclinic, saddle-node, and Bogdanov-Takens bifurcation. In order to meet the theoretical requirements, extensive numerical simulations have been presented in the conclusion.
More Related Videos
14:18Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
Published on: February 28, 2016
08:32Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels
Published on: January 28, 2022
Related Concept Videos
Second Order systems II
Damped Oscillations
Although friction and other non-conservative...
Types of Damping
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
Root Loci for Positive-Feedback Systems
The construction rules for the root locus in positive feedback systems are similar to those in...
Oscillations about an Equilibrium Position